As indicated by Luigi above, you can overlay a biplot of species correlations with the CAP axes. If you are using the PERMANOVA+ software, you can choose to use Spearman or Pearson correlations and set the level of correlation (default is 0.4). Alternatively you can manually choose which species to display. A word of warning: CAP will give you statistical correlations of species with the canonical axes, whether or not that is biologically meaningful. In other words you can obtain very strong correlations from species that are very rare but occur in only one treatment (for example). This may be meaningful or may not. As a rule of thumb, you should independently check the frequency of occurrence of species - I tend to discount correlations of species that occur in fewer than 15% of samples, or at least look closely at them to be sure the correlations are not merely statistical artefacts.

MDS is somewhat different. It is an unconstrained ordination technique that places samples in multivariate space in the most parsimonious arrangement (relative to each other). Unlike CAP, there are no a priori hypotheses. CAP ordinations come in handy when there is more going on in higher dimensions than can be accurately placed on a 2D MDS plot (in general when the stress value exceeds 0.2). Ideally you should do both if using CAP - plot an unconstrained MDS or PCO ordination too to see the "real" variation among samples.

All that said, if seeking to look at a species x samples matrix versus some suite of environmental variables, you should maybe look at a distance -based multiple regression technique like dbRDA. Again you can get biplots of species correlations with the RDA axes, but it also can run a sequential analysis that drops out the colinear predictor variables - very handy.

I do use SIMPER for related questions. I guess the answer to your question depends on what you would like to test. If you think that taking into account the presence of rare species could be important then the sensitivity to species abundance it s a problem. But you already have this problem in your CAP! A good option it s to transform, standardize, your data priory to your analysis both CAP and SIMPER. Like that you will reduce the weight of the more abundance species in your analysis. Also be careful with the index of distance use in CAP and SIMPER, there should be the same. Hope this could help!

I usually use SIMPER as an ancillary analysis to support robust tests (such as PERMANOVA) when describing patterns of species distribution. SIMPER may be OK or not depending on the aim of your research. I think you could try some alternative methods in order to get a general consensus: e.g. CAP analysis allows to overlap species contribution directly on the biplot; if you transform your dataset before, you can get an additional idea about species contribution that should be "less" driven by species abundance.

Simper is useful, but it inevitably is highly abundance biased as it is a represntation of the average % contribution of each species to a multivariate distance measure such as Bray-Curtis index; this is represented as both within-group and between-group diffrerence contributions. As such, species which have high average abundance will cointribute more highly to the difference/similarity, this is exacerbated in datasets where abundances span the range from single units to thousands, and can be affected by any transformations applied. Datasets with highly skewed abundance distributions are also affected more bythis problem. In essence it depends what you want to know, so we looked for species contriubuting to differences in an impacrt study of salmon farming in one paper (available through RG), here I don't mind Simper as impacts can be well characterised by changes in dominant taxa, but I'd be less inclined to ues the technique if I were studying effects of biodiversity where I was equally concerned with occurrence patterns of rare taxa. I also wouldn't personally ues CAP, but that's a personal preference.

Hi,

You can use SIMPER with presence/absence data (overall transformation of data before make the similarity matrix) and compare results with abundance (or a transformation of abundance) data and use both results... SIMPER allows you evaluate the species contribution to intragroups similarities and intergroup disimilarities... but if you want measure indicator value of a species, I think is better than you use the IndVal...

Best wishes,

Antonio.

From my point of view, SIMPER and CAP are very different statistical approaches. If you are interested in measure species contribution to the explained variance in the CAP model, I think that you can’t use SIMPER. But SIMPER can be used in a parallel mode, as explained above. Regards.

Hi,

Thank you very much for your answers. I had not thought about using SIMPER for presence-absence data, since I related this method to species abundance. But if I understood it good from the answers, SIMPER computation is performed on the Bray-Curtis distance matrix and thus it will show the contribution of species to the overall dissimilarity. So what matters is how the distance matrix is computed and the interpretation of SIMPER results relates to it.

Regarding CAP: would you use NMDS instead?

Thank you for mentioning IndVal, I'll have a look at it.

Best

Have you considered using Indicator Species Analysis? There are packages available in R. This might get at your question better.

Yes Indic species is a valuable R package

I would go for NMDS with bray-curtis distance and SIMPER. Maybe standardize the data first. In R, the vegan package does both analysis and a very good tutorial from Jari Oksanen is available online! Good luck!

As indicated by Luigi above, you can overlay a biplot of species correlations with the CAP axes. If you are using the PERMANOVA+ software, you can choose to use Spearman or Pearson correlations and set the level of correlation (default is 0.4). Alternatively you can manually choose which species to display. A word of warning: CAP will give you statistical correlations of species with the canonical axes, whether or not that is biologically meaningful. In other words you can obtain very strong correlations from species that are very rare but occur in only one treatment (for example). This may be meaningful or may not. As a rule of thumb, you should independently check the frequency of occurrence of species - I tend to discount correlations of species that occur in fewer than 15% of samples, or at least look closely at them to be sure the correlations are not merely statistical artefacts.

MDS is somewhat different. It is an unconstrained ordination technique that places samples in multivariate space in the most parsimonious arrangement (relative to each other). Unlike CAP, there are no a priori hypotheses. CAP ordinations come in handy when there is more going on in higher dimensions than can be accurately placed on a 2D MDS plot (in general when the stress value exceeds 0.2). Ideally you should do both if using CAP - plot an unconstrained MDS or PCO ordination too to see the "real" variation among samples.

All that said, if seeking to look at a species x samples matrix versus some suite of environmental variables, you should maybe look at a distance -based multiple regression technique like dbRDA. Again you can get biplots of species correlations with the RDA axes, but it also can run a sequential analysis that drops out the colinear predictor variables - very handy.

Thank you very much. I would like to see if species composition is related to two environmental variables (a factor and a gradient), that's why I chose to perform a constrained analysis. Something that confuses me from the answer of Trevor is that there seems to be a difference between CAP and distance-based RDA. For me it is the same. Is there truely a difference?

You are right that looking at correlation with axes may be the more meaningful for a constrained analysis. However, the idea of SIMPER is to show the contribution of different species according to a factor of interest. Thus there should be an a priori hypothesis that the factor is influencing species composition. In contrast, I see NMDS more as an exploratory method for looking at species distribution in "space". Thus the link between SIMPER analysis and NMDS is not really obvious to me. Since SIMPER is not linked to a particular statistical test and NMDS also not, I find it difficult to interpret the results of SIMPER without previously assessing if the factor of interest really explains some variance in species composition.

I agree with David - perhaps the best option for a start would be to use the Dufrêne-Legendre indicator species analysis. This would help you compute the indicator value (fidelity and relative abundance) of species in clusters or types. Use the labdsv and indicspecies packages in R, they are pretty straightforward.

Hope this helps!

Trevor speaks wisely. I personally wouldn't normalise data for a SIMPER as I'd invariably desire some contribution from differences in scale of abundance, but If I wanted an equivalent effect I'd run on pres/abs data. I run these analyses in PRIMER + PERMANOVA which offers nonparametric multivariate multiple regression and ancova equivalents. actually I've defaulted to using PERMANOVA for many awkward nonparametric analyses, especially where I want to model simplify and pool variance or perform complex contrasts.

First of all, if you are only interested in composition then you can reduce your dataset to presence/absence and dump Bray-Curtis in favour of say, Jaccard or Sorensen's index. Bear in mind though that joint absences of species will influence your distance matrix, and you have to decide if you want that.

Yes CAP and dbRDA are a little different, though both are constrained ordination techniques. RDA (reduced dimension analysis) is a graphical output of DISTLM (distance-based linear model), which is probably what I should have referred to in the first instance. The statistical procedures are different: CAP is not fitting a linear model, but conducting a canonical discriminant or canonical correspondence analysis (CDA or CCA) based on a priori specified groups (in the case of CDA) or finding the "best" correlation between your data and the predictor variables (in the case of CCA). It is quite possible to get similar output from both CAP and DISTLM - especially if the correlations are strong.

DISTLM does output proportion of variance explained by each predictor - though with only two you may find you are left with quite a bit of unexplained variance. If the predictors are in any way correlated you might find that the sequential test dumps one of them. It'll give you p values too (if you really feel the need).

Hi Valérie, I think that you could use a very simple analysis that may help you to explore the contribution of the species to your ordination pattern (CAP, nMDS, so on). The name of the test is BVStep and what it does is to find a sub-set of species that explains the multivariable patterns as the whole assemblage data. Is similar to SIMPER but the difference is that BVStep does from a continuous multivariate pattern, rather than defined clustering of samples (as SIMPER does). Basically, is spearman rank correlations to determine the minimun number of variables (i.e. taxa) that shows the highest correlation with the complete matrix. This is much more informative in the sense of searching for species as indicators and so. The routine is available in PRIMER. Hope this helps. best

Thank you, I will carefully consider your different propositions according to the question at hand. I think a representation of the data with NMDS is worthwhile anyway. Since I expect a linear response to my gradient, I should use dbRDA rather than CAP. Regarding SIMPER, indicator species analysis, or BVStep, I will have to study a little bit deeper each method :), but certainly all have their value. For BVStep I will look if there is some R alternative, because I am not a PRIMER user, but there should be.

Best

I just want to add some advice, since you mentioned that you expect a linear response to your gradient (I see that in your ordination plot will show your dots gradually separating in the space as the gradient goes) then I could suggest using the routine "seration with replication" in the RELATE routine also incorporated in PRIMER. With this you could test the linearity of your gradient by correlating your data matrix with a model matrix to see whether your gradient is so. best

Thanks Aldo that's interesting. Are you sure of the term "seration with replication"? I googled this but could not find anything corresponding.

I agree with some previous comments. I think IndVal analysis in R will be better than SIMPER. Moreover, I think PCA for your type of data is not adequate, NMDS could be the right option.

I hope this help!

NMDS is nice, but I still would like to relate species composition to my environmental variables. I could use post-hoc variable fit (envfit in vegan R package). However, this is not exactly the same as a constrained ordination, although it seems to be commonly used to explain species-environment relationships.

Hi Valérie, you will find the seriation test in the PRIMER users manual (Clarke & Gorley 2006). But this would request having the software installed. I think it is worth buying it is not very expensive. Also with PRIMER you can explore the relationship between environmetal variables and your biotic data. For example, using BIOENV routine you can explore what abiotic variable or sub-set of then correlates better with your biotic matrix. My friend just published a paper linking environmental gradientes with biotic matrices, you should have a look on it: van Son et al. 2013 The Open Marine Biology Journal 7: 14-27. cheers

I'll do thanks

Seriation with replication is described in Somerfield, P. J., Clarke K. R., Olsgard, F. (2002) A comparison of the power of categorical and correlational tests applied to community ecology data from gradient studies. J. Anim. Ecol. 71:581-593.

The original question, concerning an alleged problem with SIMPER, is based on a flawed understanding. There is no issue with SIMPER being sensitive to species abundance. The issue is really about using appropriate combinations of resemblance measure and transformation to reflect the aspects of community variation you are interested in. However, SIMPER is about contributions to similarities among groups of samples, and it looks to me like you are more interested in correlations.

A new method of looking at variables which may be relevant is Somerfield, P. J., Clarke, K. R. (2013) Inverse analysis in non-parametric multivariate analyses: distinguishing of groups of associated species which covary coherently across samples. J. Exp. Mar. Biol. Ecol. 449: 261–273. DOI:10.1016/j.jembe.2013.10.002.

Thank you Paul. You're right. Since I aim at explaining species composition by environmental variables, I should investigate correlations. Your paper sounds highly interesting, I'll read it and be happy if you don't mind I contact you for additional information if needed,

Dear Valerie may be the following paper that is in print in the journal "Community ecology" could be of your interest:

Fuzzy sets and eigenanalysis in community studies: classification and ordination are “two faces of the same coin”.

E. Feoli 1,3 and V. Zuccarello2

1. Department of Life Sciences, University of Trieste, Via Giorgieri 10, I-34127 Italy

2. Department of Sciences and Biological Technology, University of Salento, Lecce I-73100, Italy

3. Corresponding author. Tel.: +39 040 5583879, Fax: +39 040 5582011, E-mail: [email protected]

Keywords: clusters, data matrices, diagnostic value, indicator value, similarity matrices, ordination axes, vegetation

Abstract. With this paper we want to stress that, on the basis of some matrix algebra theorems, eigenvectors of similarity matrices are strictly related with clusters that we can obtain with clustering procedures applied to the same similarity matrices and that the use of fuzzy sets obtained by cluster analysis can be efficiently used as ordination axes and also as tools to measure the diagnostic value (or the indicator value) of attributes (species or other characters) of the ecological systems.

Abbreviations FS – fuzzy set, OBC-ordination based on classification, CA-correspondence analysis, PCA- principal component analysis

Introduction

Feoli (1973a) quoted a paper that was never published as it was originally written: ‘Principal component analysis to inquire on diagnostic values of characteristic species’ (Feoli, “dattiloscritto” i.e. mimeographed). In that paper the term PCA was not used in its strict technical sense, i.e. as described by Orlóci (1978) according to the R, Q and D modes, where the basic similarity matrix between attributes (R mode) or objects (Q and D modes) is a matrix of scalar product centered by rows. The term was used to indicate all methods based on eigenanalysis (including Correspondence Analysis, CA) of any symmetric matrix, centered or not. For this reason the ordination methods based on eigenanalysis were classified into two main groups, centered and non-centered PCA, as was done by Noy-Meir (1973) for ordination methods. At that time Feoli was studying matrix algebra and set theory, rather than statistics, and he found it natural to call principal components the eigenvectors of any symmetric matrix ranked by the values of the corresponding eigenvalues.

The unpublished paper by Feoli showed an example based on phytosociological relevés of Gauco-Puccinellietalia (used also by Feoli 1977a, 1977b) that the species characterizing clusters (i.e. species with high diagnostic value) have high scores negative or positive on bipolar axes (eigenvectors) obtained with eigenanalysis, while species without diagnostic values may have high scores (if common) only on the first unipolar axes and always low scores on the bipolar axes. Consequently, ordination scatter plots based on bipolar axes (such as PCA and CA) always show the common or the rare species without diagnostic value near the origin of the ordination axes, and the diagnostic species far from the origin.

I can sent you the complete manuscript if you are interested to read it.

Thank you very much. By looking at the different methods you proposed me I found a book that is really helpful and that I would recommand to all R users (and the others of course) interested in questions of community analysis (but most of you certainly already know it): Numerical Ecology with R, Borcard, Gillet & Legendre, 2011, Springer. Many methods you suggested are discussed with helpful examples. An interesting one is Kendall's W coefficient of concordance, although it may be best used with no a priori expected environmental grouping factor. I think Fuzzy sets are also mentioned.

@ Paul Somerfield: the method you suggested is highly interesting. Saddly it is only applicable with the software PRIMER that I do not have. But certainly there will be a R package arising in the next times.

@ Enrico: I would be very interested by your manuscript

Best

Dear Valerie I hope the ms. is attached best regards Enrico

Maybe you should consider using General Linear Mixed Models with zero-inflated modeling if you have many samples with zeros (absence of species). This is a recenty developed statistical method based on Bayesian statistics and Markov Chain Monte Carlo modeling developed by Alain Zuur and co-workers. Worth looking at when you have data that are strongly autocorrelated (overdispersed) or zero-inflated data. This is quite often the case in environmental data. It can deal with such datasets where multivariate models cannot.

hi

i read some comments, i agree with Boom, if you want to explain detail on species

-recognize the InVal (Anneville, et al. 2002) and on base the normality of its data, choose GLM or GAM . and in condition with many zero in data use some zero-inflated metods such as :COZIGAM, Liu & Chan, 2010) in R.

regards

I think SIMPER is fine so long as you are aware that it is more sensitive to species composition than PERMANOVA :-)

https://www.researchgate.net/post/What_are_the_criteria_for_selecting_variables_for_PCA_analysis_in_Primer_6_how_to_screen_variables